A particle moving in the x direction is being acted upon by a net force F(x)=Cx2, for some constant C. The particle moves from xi=L to xf=3L

Question

A particle moving in the x direction is being acted upon by a net force F(x)=Cx2, for some constant C. The particle moves from xi=L to xf=3L. What is ΔK, the change in kinetic energy of the particle during that time?

in progress 0
Philomena 5 years 2021-08-28T16:05:26+00:00 1 Answers 28 views 0

Answers ( )

  1. kimchi2
    0
    2021-08-28T16:07:25+00:00
    Reply

    Answer:

    Change in kinetic energy is ( 26CL³)/3

    Explanation:

    Given :

    Net force applied, F(x) = Cx²  ….(1)

    Displacement of the particle from xi = L to xf = 3L.

    The work-energy theorem states that change in kinetic energy of the particle is equal to the net amount of work is done to displace the particle.

    That is,

    ΔK = W = ∫F·dx

    Substitute equation (1) in the above equation.

    ΔK =  ∫Cx²dx

    The limit of integration from xi = L to xf = 3L, so

    \Delta K=\frac{C}{3}(x_{f} ^{3} - x_{i} ^{3})

    Substitute the values of xi and xf in the above equation.

    \Delta K=\frac{C}{3}((3L) ^{3} - L ^{3})

    \Delta K=\frac{C}{3}\times26L^{3}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )